Structural, pressure-dependent resistivity, angle resolved photoemission spectroscopy (ARPES), x-ray photoelectron diffraction (XPD) and band structure by DFT calculation have been investigated for BiSbTe₃ Topological insulator. It has been demonstrated that the Dirac point of the topological surface state (TSS) located exactly at the Fermi level. Additionally, superconductivity emerges under pressure of 8 GPa with a critical temperature of ∼2.5 K. With further increase of pressure, the superconducting transition temperature (T_c) increases and at 14 GPa it shows the maximum T_c (∼3.3 K). It has also been shown that the surface state remains unchanged under pressure and has been suggested that the origin of the superconductivity is due to the bulk state. The investigation indicates that the BiSbTe₃ has robust surface states and becomes superconductor under pressure.